Question

The section of a window consists of a rectangle surmounted by and equilateral triangle. If the perimeters be given as 10ft, find the dimensions of the window in order that the maximum amount of light may be admitted.

100 POINTS PLEASE

Answer 1

Solution

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Correct option is C)

Perimeter of window P=2y+3x=16

⇒y=

2

16−3x

​

....(1)

Area A=xy+

4

3

​

​

x

2

=

4

3

​

​

x

2

+x(

2

16−3x

​

)

A=8x+(

4

3

​

​

−

2

3

​

)x

2

dx

dA

​

=8+(

4

3

​

​

−

2

3

​

)2x

For maxima or minima,

dx

dA

​

=0

⇒4−

4

(6−

3

​

)

​

x=0.

∴x=

6−

(3)

​

16

​

=

36−3

16(6+

3

​

)

​

=

33

16(6+1.73)

​

=

33

16(7.73)

​

=

33

123.68

​

⇒x=3.75 nearly.

Now,

dx

2

d

2

A

​

=2(

4

3

​

​

−

2

3

​

)<0

Hence A is maximum.

By (1),

y=2.375

Explanation: